Full frame lens with crop body

Your lens is build for the larger format. It projects the full image into the body regardless if there is all the sensor surface to capture it or not. Naturally your original lens hood is designed to block anything else but to pass all this light that you do not really need for your image as your sensor is much smaller. If now the sun or any other source of ligt would be part of the full frame but is not included in your crop image then the hood does not block this light and your image may suffer from flares.

The following images show how that looks like. They were taken with an EOS 20D (crop 1.6, EF-S mount) and an EF 35mm 1:2 IS USM lens with the original lens hood EW-72. Exactly that happened as you can see. Its got some flares although the sun is not part of the image. Actually the sun is top right close to the sensor frame and would be within a full frame sensor's image.

For this nearly identical image I used some piece of cardboard and hold it there where the hood should have been if it was designed for crop bodies.

- no flares -

Solution: This is one of the rare usages of the zoom factor. Do apply it to your lens hood. For this 35mm lens on a body with crop 1.5 or 1.6 use a hood that was designed for about 50mm.

The same happens to zoom lenses

The manufacurers do provide hoods for zoom lenses too. Here the problem is quite similar. Naturally the hood was designed for the shortest focal length only. When you now zoom in then the hood lets more light pass than needed for your current frame. This applies especially for super zoom lenses which vary from (ultra) wide angle to tele. E.g. an 18-200 is much more vulnerable for flares caused by this effect than a 100-300 lens.

However, for lenses with large zoom factors it is advisable to buy some suitable hood for the longer focal width. You may find them from 3rd party suppliers designed for the filter mount.

E.g. for a 18-55 lens I would use the original one for 18+ mm and an additional one for about 24+ mm and a 3rd one for 35+ mm.

If you got both, use a zoom lens, that is designed for full frame used with a crop body, then do apply the crop factor too.